Large period limit

The large period limit of a periodic equation, say on a large torus $(\mathbf {R} /L\mathbf {Z} )^{d}$ denotes the limit when $L\to \infty$. Formally, this limit should converge to the same equation on the non-periodic domain $\mathbf {R} ^{d}$, though when the equation has infinite speed of propagation then the justification of this limit can be quite delicate.